The formula you have written is for when you taking angle $\omega t$ from horizontal $x$-axis but in your case, the point is starting from the y-axis thus it's necessary to take the angle $\omega t$ from the positive y-axis. This will turn your formula to $$y=r\cos(\omega t)$$ $$x=r\sin(\omega t)$$ Now you can proceed from here. :)

The formula you have written is for when you taking angle $\omega t$ from horizontal $x$-axis but in your case, the point is starting from the y-axis thus it's necessary to take the angle $\omega t$ from the positive y-axis. This will turn your formula to $$y=r\cos(\omega t)$$ $$x=r\sin(\omega t)$$ Now you can proceed from here. :)

We are given $\omega=\pi/30$ rad-sec$^{-1}$ After $30$ sec $$y=2\cos\left(\frac{\pi}{30}\cdot 30\right)=2\cos(\pi)=-2$$ and $$x=2\sin\left(\frac{\pi}{30}\cdot 30\right)=2\sin(\pi)=0$$